Social systems produce complex and nonlinear relationships in the indicator variables that describe them. Traditional statistical regression techniques are commonly used in the social sciences to study such systems. These techniques, such as standard linear regression, can prevent the discovery of the complex underlying mechanisms and rely too much on the expertise and prior beliefs of the data analyst. In this thesis, we present two methodologies that are designed to allow the data to inform us about these complex relations and provide us with interpretable models of the dynamics.

The first methodology is a Bayesian approach to analysing the relationship between indicator variables by finding the parametric functions that best describe their interactions. The parametric functions with the highest model evidence are found by fitting a large number of potential models to the data using Bayesian linear regression and comparing their respective model evidence. The methodology is computationally fast due to the use of conjugate priors, and this allows for inference on large sets of models. The second methodology is based on a Gaussian processes framework and is designed to overcome the limitations of the first modelling approach. This approach balances the interpretability of more traditional parametric statistical methods with the predictability and flexibility of non-parametric Gaussian processes.

This thesis contains four papers where we apply the methodologies to both real-life problems in the social sciences as well as on synthetic data sets. In paper I, the first methodology (Bayesian linear regression) is applied to the classic problem of how democracy and economic development interact. In paper II and IV, we apply the second methodology (Gaussian processes) to study changes in the political landscape and demographic shifts in Sweden in the last decades. In paper III, we apply the second methodology on a synthetic data set to perform parameter estimation on complex dynamical systems.